Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;


public class CF815A {
	static int n;
	static int m;
	static int[][] arr;
	static int[] rows;
	static int[] cols;
	public static void main(String[] args) {
		FastReader fr = new FastReader();
		n = fr.nextInt();
		m = fr.nextInt();
		arr = new int[n][m];
		boolean swapped = false;
		for(int i=0;i<n;i++)
		{
			for(int j=0;j<m;j++)
			{
				arr[i][j] = fr.nextInt();
			}
		}
		if(m<n)
		{
			int[][] new_arr = new int[m][n];
			for(int i=0;i<m;i++)
				for(int j=0;j<n;j++)
					new_arr[i][j] = arr[j][i];
			int temp = m;
			m = n;
			n = temp;
			arr = new_arr;
			swapped = true;
		}
		rows = new int[n];
		cols = new int[m];
		Arrays.fill(rows, Integer.MAX_VALUE);
		Arrays.fill(cols, Integer.MAX_VALUE);
		int[] rows_temp = new int[n];
		int[] cols_temp = new int[m];
		Arrays.fill(rows_temp, Integer.MAX_VALUE);
		Arrays.fill(cols_temp, Integer.MAX_VALUE);
		for(int i=0;i<n;i++)
		{
			for(int j=0;j<m;j++)
			{

				cols[j] = Math.min(cols[j],arr[i][j]);
				rows[i] = Math.min(rows[i],arr[i][j]);
				rows_temp[i] = rows[i];
			}
		}
		int ans = 0;
		ArrayList<String> al = new ArrayList<String>();
		int[][] temp_arr = new int[n][m];
		for(int i=0;i<n;i++)
		{
			while(rows_temp[i]>0)
			{
				for(int j=0;j<m;j++)
				{
					temp_arr[i][j]++;
				}
				rows_temp[i]--;
				//System.out.println("row "+i);
				if(!swapped)
					al.add("row "+(i+1));
				else
				al.add("col "+(i+1));
				ans++;
			}
		}
		for(int i=0;i<n;i++)
		{
			for(int j=0;j<m;j++)
			{
				cols_temp[j] = Math.min(cols_temp[j],temp_arr[i][j]);
			}
		}
		for(int i=0;i<m;i++)
		{
			while(cols[i]-cols_temp[i]>0)
			{
				for(int j=0;j<n;j++)
				{
					temp_arr[j][i]++;
				}
				cols_temp[i]++;
				//System.out.println("col "+i);
				if(!swapped)
					al.add("col "+(i+1));
				else
					al.add("row "+(i+1));
				ans++;
			}
		}
		boolean error = false;
		for(int i=0;i<n;i++)
		{
			for(int j=0;j<m;j++)
			{
				if(temp_arr[i][j]==arr[i][j])
					continue;
				else
				{
					error = true;
					break;
				}
			}
		}
		if(error)
			System.out.println("-1");
		else
		{
			System.out.println(ans);
			al.forEach((s)->System.out.println(s));
		}
	}

	//Better IO Class
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public Double nextDouble() {
			return Double.parseDouble(next());
		}

		public Float nextFloat() {
			return Float.parseFloat(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				System.out.println(e);
			}
			return str;
		}
	}
}